Two “severely overweight” children were taken into care after their weight didn't reduce in six months despite the council paying for Fitbits and gym memberships for them.
Judge Gillian Ellis has ruled the youngsters should go into long-term foster care - and described the case as "very sad and unusual".
West Sussex County Council, who had responsibility for the children's welfare, had provided Fitbits, and paid for gym membership, and the family had been involved with Weight Watchers.
But Judge Ellis said months after family court proceedings began there had been no reduction in the children's weight.
The judge said the children's parents had not seemed to understand "the seriousness" of concerns raised by social services staff and had failed to "set boundaries" or "promote healthy eating and exercise".
She said the children needed the chance to "learn ways of living more healthily" and to "improve their health by losing weight".
Details of the case emerged in a ruling by Judge Ellis published online on Wednesday.
The judge had considered evidence at a private family court hearing in Sussex late in 2020.
She said the family could not be identified in media reports of the case.
The judge said there were also concerns about poor home conditions and a lack of guidance on personal care.
"Everyone agrees that this is a very sad and unusual case, of a loving family, where the parents meet many of the basic needs of the children, but the local authority has been concerned that the parents are not meeting the children's health needs, in that both children are severely overweight, and the parents have shown an inability to help the children manage this condition," said the judge in her ruling.
"The case was such an unusual one because the children had clearly had some very good parenting, as they were polite, bright, and engaging."
She added: "The children were supposed to provide recordings from their Fitbits but this had not been done.
"The mother blamed lockdown for the inability to exercise but exercise could still be taken in the home or by walking outside.
"The attendance of the family at Weight Watchers had been inconsistent."